Weak solutions for singular quasilinear elliptic systems

We investigate the quasilinear elliptic system {-Delta(m)u = u(-p)v(-q), u > 0 in Omega, -Delta(m)v = u(r)v(-s), v > 0 in Omega, u = v = 0 on partial derivative Omega, where Omega subset of R-N(N >= 1) is a bounded and smooth domain, 1 < m < infinity, p, q, r, s > 0. Under certain conditions imposed on the exponents, we obtain the existence and uniqueness of a weak solution (u, v) with u, v is an element of W-0(1,m) (Omega) boolean AND C(Omega). We also investigate the W-0(1,tau) (Omega) regularity of solution and determine the optimal range of tau >= m for such regularity.